A371531 a(n) is the multiplicative order of A053669(n) modulo n.

1, 1, 2, 2, 4, 2, 3, 2, 6, 4, 10, 2, 12, 6, 4, 4, 8, 6, 18, 4, 6, 5, 11, 2, 20, 3, 18, 6, 28, 4, 5, 8, 10, 16, 12, 6, 36, 18, 12, 4, 20, 6, 14, 10, 12, 11, 23, 4, 21, 20, 8, 6, 52, 18, 20, 6, 18, 28, 58, 4, 60, 30, 6, 16, 12, 10, 66, 16, 22, 12, 35, 6, 9, 18, 20

Offset: 1

Author

Darío Clavijo, Mar 26 2024

Keywords

• nonn

Crossrefs

Cf. A002326, A053669, A284723.

Programs

Mathematica

a[n_] := Module[{p = 2}, While[Divisible[n, p], p = NextPrime[p]]; MultiplicativeOrder[p, n]]; Array[a, 75] (* Amiram Eldar, Mar 26 2024 *)

PARI

f(n) = forprime(p=2, , if(n%p, return(p))); \\ A053669
a(n) = znorder(Mod(f(n), n)); \\ Michel Marcus, Mar 26 2024

Python

from sympy.ntheory.residue_ntheory import n_order
from sympy import nextprime
def a(n):
  if n == 1: return 1
  if n & 1 == 1: return n_order(2, n)
  p = 2
  while n % p == 0:
    p = nextprime(p)
  return n_order(p, n)
print([a(n) for n in range(1, 76)])

Formula

a(2k+1) = A002326(k) for k >= 1.

a(2k) = ord(A284723(k), 2k).